Groups in Geometry

首席研究员将研究最近发现的新的无限几何族。此外，PI将研究局部生成的几何，将一些早期的结果推广到特征二。这个区域与有限单群的分类有一定的关系。最后，PI将研究无穷秩经典几何的点-线特征。群论领域是对称的数学理论，并与许多其他学科相互作用，例如数学之外的物理和化学，数学内部的编码理论，数论和几何。研究者的特定领域是有限群和几何。这是一门古老的学科，但仍面临着许多未解决的问题，也有许多突破的机会。

SHULT 9701188 The principal investigator will investigate new infinite families of geometries recently discovered. Also, the PI will study locally-generated geometries generalizing some earlier results to characteristic two. This area bears some relation to the classification of the finite simple groups. Finally, the PI will look at point-line characterizations of classical geometries of infinite rank. The field of group theory is the mathematical theory of symmetry and interacts with many other disciplines, for example physics and chemistry outside of mathematics, coding theory, number theory and geometry inside mathematics. The investigator's particular area is finite groups and geometries. It is an old subject but still facing great unsolved problems and with many opportunities for breakthroughs.